Wielowymiarowa analiza wariancji - MANOVA
MULTIVARIATE ANALYSIS OF VARIANCE - MANOVA
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The paper describes a model of the multivariate analysis of variance (MANOVA). First, we outline differences between this method and the univariate analysis of variance (ANOVA). We present basic repeated measures designs and point to the research designs that provide data which can be analyzed only with the MANOYA models. We describe formal structure of the MANOVA model and provide its basic definitions. We show how these definitions are related to terms of ANOVA. Development of the ANOVA logic into the MANOYA model is shown in relation to a discussion on independence between expected values of variables and their bivariate correlations (more precisely - means of variables and Pearson product-moment correlation coefficients). We explain how the assumptions, null hypotheses and test statistics of MANOVA have been developed from the ANOVA model. We point to the inconclusiveness of the formal MANOYA solution (lack of the one, established, test statistic) and show these test statistics which appeared most often in the statistical software in the last twenty years. We illustrate formalities of the model with one fictional example of a simple one-way MANOVA. Ali test statistics introduced in this paper were calculated by hand and compared with SPSS output. Moreover, an example of application of multivariate analysis of variance in psychological research was portrayed, using a study on evaluation of managers' performance. In this example, we emphasize reasons why it is necessary to complement MANOVA with another method: discriminant analysis.
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